Think of prog rock and many listeners still envision “unnecessarily long songs, full of fantastical lyrics, played by people in capes,” said Jakko Jakszyk, singer of King Crimson, a band often seen as typifying that genre.

Yet, that foppish and effete image stands in stark contrast to the muscular and radical sounds Crimson has actually produced over the past four decades. Throughout a dizzying range of incarnations, the band led by visionary guitarist Robert Fripp has played music with an intensity as raw as punk, a scope as wild as free jazz and a sophistication as refined as classical music. Even amid the rarefied world of so-called prog, Crimson stands out for their extreme approach. “When people hear our records, they either say ‘Oh, that’s King Crimson,’ or they say, ‘What the is that?” Jakszyk said.

In some ways, the band’s latest incarnation is their most puzzling yet. It involves the highest number of members they’ve ever had: eight, including three drummers. It’s also the first Crimson incarnation to integrate material from every phase in their long and complex career. The band’s latest live set, “Radical Action to Unseat the Hold of Monkey Mind,” puts special emphasis on material from Crimson’s first six albums, released between 1969 and ‘74, which represents their most fast-changing and far-reaching era. The band will perform such classics at four area shows, including Manhattan’s Beacon Theatre (Nov. 17-18).

Besides Fripp, the lineup includes another prized player from the ‘70s: sax and flute player Mel Collins. “This is the band that gives me the most freedom to play the way I want to play,” said Collins, who has performed with everyone from Tina Turner to The Rolling Stones. (He played that sax break on “Miss You.”)

Collins will be joined in this musical maelstrom by Crimson’s bassist since the ‘80s, Tony Levin; their drummer since the ’90s, Pat Mastelotto; and singer Jakszyk, who has fronted the group and mirrored Fripp on guitar for the past four years. Fripp (who doesn’t do interviews while on tour), has never been happier with a Crimson incarnation, according to Collins. “He actually smiles on stage,” he says.

That’s a shock considering the early, stern image of both Crimson and Fripp. When the group’s debut album, “In the Court of the Crimson King,” appeared in the fall of 1969, it out-freaked even the hippie freaks. Its opening track, “21st Century Schizoid Man,” howled out a dystopian rage, delineated by proto-speed-metal guitar riffs, brutal stop-start beats and a distorted vocal from original vocalist Greg Lake that sounded like a voice from hell. “We do push everything to the extreme,” Collins said with a laugh.

Even the album’s cover, with its screaming red face, relieved by no text, registered alarm. At the same time, the band made sure to contrast its most harsh and speedy passages with songs of exquisite tranquility. “The dynamics are fantastic,” Collins said.

Nearly every one of Crimson’s early albums featured a different sound, aided by the ever-changing lineup. Part of the turnover had to do with Fripp’s controlling nature at the time. “He was hard to work with,” Collins said. “It was so intense in the early ‘70s, I was on the verge of a nervous breakdown. Robert used to sit on the other side of the stage and if you made a mistake, you’d get this look from him that could kill.”

At the same time, the musicians always respected Fripp’s genius and daring. Guitar breaks weren’t just flashes of notes. Each had its own texture and choreography, and not one sounded like another. “As musicians, we all strive not to play the same thing twice,” Collins said.

That holds to this day. Innovative arrangements grace all the new versions of the songs, and they all feature wide swathes of improvisation. A piece like “Sailor’s Tale” features a generous sax solo modeled after the “Bitches Brew” era of Miles Davis, while their “Lizard Suite” runs from the double-Mellotron shock and awe of “Cirkus” to the orchestral sweep of the “Lizard” title track. “We know how a song starts and how it ends, but not how we’re going to get there,” Jakszyk said.

Jakszyk’s vocals both refer to and play with the past. His timbre can recall that of former Crimson singers John Wetton and Boz Burrell, yet he retains his own character. The greatest twist for the current band comes in the nuanced approach of the drum trio, who appear at the front of the stage. “You can’t have three drummers just going hell for leather,” Collins said. “There’s a choreography there.”

Collins said the audience for their sound has widened over the years. Old fans bring their teenage children and “there are women now,” he said.

The band hasn’t gained many hip-hop fans, however, though “Schizoid Man” was prominently sampled in Kanye West’s song “Power,” which later became ubiquitous through a cologne ad. Even so, there’s a freshness to the current band that has encouraged a bright future. “Robert is talking about touring until 2023,” Collins said. “This band has always changed and evolved. That’s why there’s no stopping it.”